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we must think of him making a thorough, understanding study
of the excessively abstract Mecanique analytique of Lagrange,
in which there is not a single diagram to illuminate the analysis
from beginning to end. Yet Boole, self-taught, found his way
and saw what he was doing. He even got his first contribution to
mathematics out of his unguided efforts. This was a paper on
the calculus of variations.
Another gain that Boole got out of all this lonely study
deserves a separate paragraph to itself. He discovered invari-
ants. The significance of this great discovery which Cayley and
Sylvester were to develop in grand fashion has been sufficiently
explained; here we repeat that without the mathematical
theory of invariance (which grew out of the early algebraic
work) the theory of relativity would have been impossible.
Thus at the very threshold of his scientific career Boole noticed
something lying at his feet which Lagrange himself might
easily have seen, picked it up, and found that he had a gem of
the first water. That Boole saw what others had overlooked was
due no doubt to his strong feeling for the symmetry and beauty
of algebraic relations  when of course they happen to be both
symmetrical and beautiful; they are not always. Others might
have thought his find merely pretty. Boole recognized that it
belonged to a higher order.
Opportunities for mathematical publication La Boole's day
were inadequate unless an author happened to be a member of
some learned society with a* journal or transactions of its own.
Luckily for Boole, The Cambridge Mathematical Journal, under
the able editorship of the Scotch mathematician, D. F. Gregory,,
was founded in 1837. Boole submitted some of his work. Its
originality and style impressed Gregory favourably, and a cor-
dial mathematical correspondence began a friendship which
lasted out Boole's life.
It would take us too far afield to discuss here the great con-
tribution which the British school was making at the tune to
the understanding of algebra as algebra, that is, as the abstract
development of the consequences of a set of postulates without
necessarily any interpretation or application to 'numbers* or
anything else, but it may be mentioned that the modern eon-